Design and analysis of two discrete-time ZD algorithms for time-varying nonlinear minimization

Abstract

Nonlinear minimization, as a subcase of nonlinear optimization, is an important issue in the research of various intelligent systems. Recently, Zhang et al. developed the continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear minimization. Based on this previous work, another two discrete-time ZD (DTZD) algorithms are proposed and investigated in this paper. Specifically, the resultant DTZD algorithms are developed for time-varying nonlinear minimization by utilizing two different types of Taylor-type difference rules. Theoretically, each steady-state residual error in the DTZD algorithm changes in an O(τ 3) manner with τ being the sampling gap. Comparative numerical results are presented to further substantiate the efficacy and superiority of the proposed DTZD algorithms for time-varying nonlinear minimization.